Mathematical and numerical study of an inverse source problem for the biharmonic wave equation

TL;DR

This paper investigates the inverse source problem for the biharmonic wave equation, characterizing radiating and non-radiating sources, and proposes a Fourier series-based numerical reconstruction method validated by experiments.

Contribution

It provides a mathematical characterization of sources and introduces a novel numerical method for source reconstruction using multi-wavenumber data.

Findings

Unique determination of radiating sources from boundary measurements

Lipschitz stability estimate for source reconstruction

Numerical experiments demonstrating method accuracy and efficiency

Abstract

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into a radiating source and a non-radiating source. The radiating source can be uniquely determined by Dirichlet boundary measurements at a fixed wavenumber. Moreover, we derive a Lipschitz stability estimate for determining the radiating source. On the other hand, the non-radiating source does not produce any scattered fields outside the support of the source function. Numerically, we propose a novel source reconstruction method based on Fourier series expansion by multi-wavenumber boundary measurements. Numerical experiments are presented to verify the accuracy and efficiency of the proposed method.